Businessman Donald Trump announced June 16 at his Trump Tower in New York City that he is seeking the Republican presidential nomination. This ends more than two decades of flirting with the idea of running for the White House.

"So, ladies and gentlemen, I am officially running for president of the United States, and we are going to make our country great again," Trump told the crowd at his announcement.

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Sen. Ted Cruz of Texas has made a name for himself in the Senate, solidifying his brand as a conservative firebrand willing to take on the GOP's establishment. He announced he was seeking the Republican presidential nomination in a speech on March 23.

"These are all of our stories," Cruz told the audience at Liberty University in Virginia. "These are who we are as Americans. And yet for so many Americans, the promise of America seems more and more distant."

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Ohio Gov. John Kasich joined the Republican field July 21 as he formally announced his White House bid.

"I am here to ask you for your prayers, for your support ... because I have decided to run for president of the United States," Kasich told his kickoff rally at the Ohio State University.

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Hillary Clinton launched her presidential bid on April 12 through a video message on social media. The former first lady, senator and secretary of state is considered the front-runner among possible Democratic candidates.

"Everyday Americans need a champion, and I want to be that champion -- so you can do more than just get by -- you can get ahead. And stay ahead," she said in her announcement video. "Because when families are strong, America is strong. So I'm hitting the road to earn your vote, because it's your time. And I hope you'll join me on this journey."

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Sen. Bernie Sanders, an independent from Vermont who caucuses with Democrats, announced his run in an email to supporters on April 30. He has said the United States needs a "political revolution" of working-class Americans to take back control of the government from billionaires.

"This great nation and its government belong to all of the people and not to a handful of billionaires, their super PACs and their lobbyists," Sanders said at a rally in Vermont on May 26.

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But the Republican delegate count is about to become a national obsession. Ohio Gov. John Kasich's win in his home state -- and 66 delegates -- makes Trump's path to the nomination more difficult, and will have everyone in the political world looking for their calculator.

Here are five takeaways from Tuesday's contests:

Clinton's pivot, take two

After her big Super Tuesday wins two weeks earlier, Clinton sought to pivot to the general election. She dropped her usual attacks on Sanders and started trying to smooth things over with his younger, more liberal supporters.

A steadier Clinton campaign made up for that loss, and then some, by crushing Sanders in Florida, North Carolina and Ohio on Tuesday, denying him a repeat. She also won Illinois and as of 2 a.m. was battling Sanders in Missouri.

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And afterward, Clinton -- who knows Sanders won't be dropping out anytime soon -- turned her eyes to November, and to Trump. The message to Democrats: The general election is here, and I'm going to stand up to the GOP front-runner.

She hammered Trump repeatedly during her speech in West Palm Beach, Florida, only a few minutes from Trump's resort there, saying at one point: "When we hear a candidate for president call for rounding up 12 million immigrants, banning Muslims from entering the United States, when he embraces torture, that doesn't make him strong, it makes him wrong."

Another big night for Trump

Trump won big -- routing Marco Rubio in Florida and running up the score in Illinois and North Carolina, while duking it out to the end with Cruz in Missouri.

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This was a defiant candidate. The violence that erupted at his rally in Chicago last weekend didn't stop him from winning the state. The media criticism led him only to take a whack at "disgusting reporters" and leave without taking a single question, even though his campaign had advertised his election-night event as a "press conference."

As the volume and fear about Trump rose to a new level, once again the Republican front-runner gets to say: Scoreboard.

Perhaps the best evidence of Trump's supreme confidence: Embattled campaign manager Corey Lewandowski, accused by a female reporter from the pro-Trump outlet Breitbart of grabbing her during a rally last week, was parked on stage next to Trump, who gave him a shout-out.

"Corey -- good job, Corey. Great job," Trump said.

Kasich's narrow road to Cleveland

So Kasich won his home state of Ohio, and all 66 of its delegates. It was an impressive victory over Trump.

But where does he go from here?

It's the first time Kasich has won a state, and he's far behind Trump and Cruz in the delegate race. He's made big bets on two other states, New Hampshire and Michigan, and he lost them both. If he can't win there, it's not clear where he can win — except for as a dark horse at the Republican National Convention in Cleveland in July.

But there are hurdles ahead for a candidate who will now face more intense scrutiny. Trump has relentlessly attacked the Ohio governor. Ted Cruz will likely hammer his decision to expand Medicaid under Obamacare. And his Not-Quite-Mr.-Nice-Guy persona from his Capitol Hill days could do him damage.

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Kasich is betting on strong showings in states that award delegates proportionally, like New York, Connecticut, Oregon and Washington, and the winner-take-alls including Wisconsin, Maryland, Pennsylvania, Indiana and California.

At the convention, Kasich's campaign said in a memo, Rubio's delegates are likely to side with the Ohio governor, "bringing the three candidates very close to parity on a second ballot."

From there, he'd make the argument that he's the best-equipped candidate to take on Clinton.

Kasich's message has been overwhelmingly positive, but he did begin drawing some implicit contrasts with Trump on Tuesday night.

"It's about pulling us together, not pulling us apart," he said.

In another Trump-focused line, Kasich said: "I will not take the low road to the highest office in the land."

A contested convention is more probable

Trump's big night still wasn't enough to stave off the likelihood of a contested convention in Cleveland.

Kasich seizing Ohio's 66 delegates complicates things for Trump. Even after winning 18 of the first 27 states with Missouri still counting, Trump needs to capture about three out of every five remaining delegates to win the 1,237 necessary to claim the GOP nomination outright.

With Cruz and Kasich continuing on, that won't be easy.

Cruz, in particular, represents a pesky challenge. He argued Tuesday night -- as he has each of the past Tuesdays -- that he and Trump are the only candidates with a shot at the nomination.

Some are convinced that allowing him to advance to the general election would permanently damage the party. Some -- particularly those those who have for president or are still in the race -- are still convinced that there's some alternative option. And some believe denying the will of the voters on the convention floor would destroy the party.

Aware of the challenge he faces, Trump talked party unity on Tuesday night from his Mar-A-Lago estate in Florida -- name-dropping House Speaker Paul Ryan and Senate Majority Leader Mitch McConnell.

"We need to bring our party together," Trump said.

Rubio's 2020 play

Rubio knew his path to the Republican nomination was non-existent once Trump crushed him in Florida.

So he made a big bet on his political future: He went down swinging against Trump, hoping that a rebalancing might swing the Republican pendulum back in his direction in the future.

"I ask the American people, do not give in to the fear. Do not give in to the frustration," Rubio said.

Of his own campaign, Rubio said, "I chose a different path, and I'm proud of that."

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Make no mistake: Rubio's Florida loss didn't just mark the end of his candidacy; it's the defining moment in the electorate's total repudiation of the GOP's efforts to reboot -- with a more inclusive, optimistic message aimed at minority populations -- after its loss in 2012.

Still, at only 44, Rubio's political star could very well rise again.

And while he won't stray far from the conservative movement -- in his exit speech, he railed against Washington elites -- his calculus depends on Trump ultimately faltering, likely in the general election.

Republican operative Rick Wilson made that much clear on Twitter, when he compared Rubio's 2016 campaign to Ronald Reagan's unsuccessful primary against President Gerald Ford in 1976 -- four years before Reagan began eight years of Republican rule and influenced an entire generation of young conservatives.